Hi, I've found a proof from given It reads: .
And taking the square root it's supposed to grant the result.
Now, I do not see why
Thanks in advance
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The statement is equivalent to since they are contrapositives. Is it clear to you that ?
Given Now I need information for because , and that's the piece that I need.
I'm sorry but I still don't get it. Thanks for your post.
Looking at this idea from a calculus perspective: the square root function is everywhere increasing and positive on its domain. Therefore, it preserves order.
Well what you have written is fine. Given we have that now provided we have that
Originally Posted by Ruun Now, I do not see why I do not understand what exactly you are asking for.
However, is clearly false. It is true that .
Is it also the case that
If so, the proof seems to work.
Yes, it is the case.
Well the proof says taking square root, and I didn't find an argument to believe in that, and this is the point I'm looking for,
Reply to Plato @ Post #6:
In this case, the things we're taking the square roots of are all positive. The step in question is this one:
It is also true that , at least in the Euclidean or norm.
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